Please note that this is pretty much a negative criticism post, rather than a balanced review as mentioned in this thread. Also be aware that stuff posted here may be highly subjective.
Please feel free to criticise this post, however.

Though not really detrimental*, htmlspecialchars is unnecessary here.
* Usernames cannot contain HTML special characters except for the double-quote, but the MyBB parser unescapes it automatically, so largely a moot point

PHP Code:

$pmsubject="New member referred by you.";$pm_message="Thanks for referring me. Check out my profile ";

The plugin makes use of language files, but these are hard coded...

There's no limit to the number of users displayed in the referrers list. Unlikely to be many, I presume, but may be worth consideration

Thank you for the review. I did not know about the usernames being already escaped; I was a bit paranoid about the username maybe being tampered with.

I will go fix those things. I must say,I was thinking that maybe there should be a setting where the last 6 referrals should show on profile with a link to show more as with a lot of referrals it gets crowded pretty fast.

Most of those could not make any difference in your board where, IIRC, yo do not use SEF urls and users with small boards will probably not even notice/care for the others but since you are releasing this to the public I felt just like sharing my thoughts.

Third point is about the correct code and hook to use to make your plugin more friendly (using the correct hook on case, somehow, an user is created outside the registration page and a referrer is set, for example) and use less code.

On the send_pm Looking at the code, my code is a duplicate of it, so I agree its wasted code - a pull request in github might be nice. The memprofile tip is something I will use as I did notice that happening.

I have several forums; I think I tried it on an SEO'd forum and the link in the pm worked... but hey, it's a free plugin, it wont harm the board (ie its not likely to get exploited) , and if someone doesn't like it no doubt there are more like it. You might even have one.